math_mod/primitive_root_64bit.hpp

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• Last update: 2025-06-06 16:34:11+09:00
• Include: #include "math_mod/primitive_root_64bit.hpp"

Depends on

• math/is_prime.hpp
• math/prime_factorize.hpp
• math_mod/pow_mod.hpp
• math_mod/pow_mod.hpp
• modint/mont_arb.hpp
• random/gen.hpp
• random/gen.hpp
• random/seed.hpp
• type_traits/integral.hpp
• type_traits/io.hpp

Required by

• math/group/rolling_hash.hpp
• random/hash.hpp
• 文字の一点更新が可能文字列に対する動的なローリングハッシュ (string/dynamic_rolling_hash.hpp)
• 文字の変更が行われない文字列に対する静的なローリングハッシュ (string/static_rolling_hash.hpp)

Verified with

• verify/aoj/aoj_alds1_14_b.test.cpp
• verify/unit_test/monoid.test.cpp
• verify/yosupo_math/primitive_root.test.cpp
• verify/yosupo_string/string_z_roliha.test.cpp

Code

#ifndef KK2_MATH_MOD_PRIMITIVE_ROOT_64BIT_HPP
#define KK2_MATH_MOD_PRIMITIVE_ROOT_64BIT_HPP 1

#include "../math/prime_factorize.hpp"
#include "../random/gen.hpp"
#include "pow_mod.hpp"

namespace kk2 {

long long primitive_root_64bit(long long p) {
    if (p == 2) return 1;
    if (p == 3) return 2;

    auto f = factorize(p - 1);
    for (long long g{}; g = random::rng(2, p - 1), 1;) {
        if ([&]() {
                for (auto &&[q, e] : f)
                    if (pow_mod<__int128_t>(g, (p - 1) / q, p) == 1) return false;
                return true;
            }())
            return g;
    }
    return -1;
}

template <class mint> long long primitive_root_mint() {
    if (mint::getmod() == 2u) return 1;
    if (mint::getmod() == 3u) return 2;

    long long p = mint::getmod();

    auto f = factorize(p - 1);
    for (mint g; g = random::rng(2, p - 1), 1;) {
        if ([&]() {
                for (auto &&[q, e] : f)
                    if (g.pow((p - 1) / q) == mint(1)) return false;
                return true;
            }())
            return g.val();
    }
    return -1;
}

} // namespace kk2

#endif // KK2_MATH_MOD_PRIMITIVE_ROOT_64BIT_HPP

Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.12.0/x64/lib/python3.12/site-packages/onlinejudge_verify/documentation/build.py", line 71, in _render_source_code_stat
    bundled_code = language.bundle(stat.path, basedir=basedir, options={'include_paths': [basedir]}).decode()
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.0/x64/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus.py", line 187, in bundle
    bundler.update(path)
  File "/opt/hostedtoolcache/Python/3.12.0/x64/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus_bundle.py", line 401, in update
    self.update(self._resolve(pathlib.Path(included), included_from=path))
  File "/opt/hostedtoolcache/Python/3.12.0/x64/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus_bundle.py", line 401, in update
    self.update(self._resolve(pathlib.Path(included), included_from=path))
  File "/opt/hostedtoolcache/Python/3.12.0/x64/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus_bundle.py", line 401, in update
    self.update(self._resolve(pathlib.Path(included), included_from=path))
  File "/opt/hostedtoolcache/Python/3.12.0/x64/lib/python3.12/site-packages/onlinejudge_verify/languages/cplusplus_bundle.py", line 312, in update
    raise BundleErrorAt(path, i + 1, "#pragma once found in a non-first line")
onlinejudge_verify.languages.cplusplus_bundle.BundleErrorAt: type_traits/integral.hpp: line 4: #pragma once found in a non-first line

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